Not impossible, just unlikely. Collisions can exist in theory in any hashing algorithm (though it may be a 2^2048 large address space or something)

Yup. Further, you can generate billions of keys until you find one where the public key matches some sequence you define beforehand. I brute forced one that starts with "superkuh". It only takes some tens of minutes to an hour or two on a GPU from 2010.

As long as you keep the private keys private you get traffic to that public key and "own" the domain.